/// <summary>
/// If you're willing to spend 'resourcesAvailable' and want to buy something with
/// additively increasing cost each purchase (start at priceStart, add by priceAdd,
/// already own currentOwned), how much of it can you buy?
/// </summary>
public static BigDouble AffordArithmeticSeries(BigDouble resourcesAvailable, BigDouble priceStart,
BigDouble priceAdd, BigDouble currentOwned)
{
var actualStart = priceStart + currentOwned * priceAdd;
//n = (-(a-d/2) + sqrt((a-d/2)^2+2dS))/d
//where a is actualStart, d is priceAdd and S is resourcesAvailable
//then floor it and you're done!
var b = actualStart - priceAdd / 2;
var b2 = BigDouble.Pow(b, 2);
return(BigDouble.Floor(
(BigDouble.Sqrt(b2 + priceAdd * resourcesAvailable * 2) - b) / priceAdd
));
}
public static BigDouble Sqrt(this BigDouble value)
{
return(BigDouble.Sqrt(value));
}